Supernova simulations confront SN 1987A neutrinos

We return to interpreting the historical SN 1987A neutrino data from a modern perspective. To this end, we construct a suite of spherically symmetric supernova models with the prometheus-vertex code, using four different equations of state and five choices of final baryonic neutron-star (NS) mass in the $1.36–1.93M_{\odot }$ range. Our models include muons and proto-neutron star (PNS) convection by a mixing-length approximation. The time-integrated signals of our $1.44M_{\odot }$ models agree reasonably well with the combined data of the four relevant experiments, IMB, Kam-II, BUST, and LSD, but the high-threshold IMB detector alone favors a NS mass of $1.7–1.8M_{\odot }$, whereas Kam-II alone prefers a mass around $1.4M_{\odot }$. The cumulative energy distributions in these two detectors are well-matched by models for such NS masses, and the previous tension between predicted mean neutrino energies and the combined measurements is gone, with and without flavor swap. Generally, our predicted signals do not strongly depend on assumptions about flavor mixing, because the PNS flux spectra depend only weakly on antineutrino flavor. While our models show compatibility with the events detected during the first seconds, PNS convection and nucleon correlations in the neutrino opacities lead to short PNS cooling times of 5–9 s, in conflict with the late-event bunches in Kam-II and BUST after 8–9 s, which are also difficult to explain by background. Speculative interpretations include the onset of fallback of transiently ejected material onto the NS, a late phase transition in the nuclear medium, e.g., from hadronic to quark matter, or other effects that add to the standard PNS cooling emission and either stretch the signal or provide a late source of energy. More research, including systematic 3D simulations, is needed to assess these open issues.

Figure 1

Evolution of the ${\overline{\nu }}_e$ luminosities (top) and average energies (bottom) for our models with SFHo EOS and different NS masses for the three main emission phases: shock breakout and prompt ${\nu }_e$ burst (left), postbounce accretion and shock revival (middle), and PNS cooling (right). Note the different time and luminosity scales. Here and in the following similar plots, the neutrino emission properties are shown for a distant observer at rest in the reference frame of the source.

Figure 2

Evolution of the signal properties of different neutrino species for our model 1.44-SFHo during the three main emission phases of Fig. 1. The upper three rows display the luminosities, average energies, and spectral pinching parameters for the $\alpha$-fit (Appendix pp5). While the model simulations were performed with six-species transport, the results are plotted here for ${\nu }_e$ and ${\overline{\nu }}_e$ as well as ${\nu }_x$ and ${\overline{\nu }}_x$, whose quantities are defined as arithmetic means of those of the $\mu$ and $\tau$ flavors. The bottom row shows the event rates by IBD predicted for Kam-II and IMB, once assuming no flavor conversion (i.e., detection of the ${\overline{\nu }}_e$ flux) and another time for a complete flavor swap (i.e., detection of the ${\overline{\nu }}_x$ flux). For IMB, the average trigger rate was used as discussed later in the text.

Figure 3

Evolution of the ${\overline{\nu }}_e$ luminosities (top) and average energies (bottom) during the three main neutrino emission phases of Fig. 1 for our $1.44M_{\odot }$ models with different nuclear EOSs as indicated in the legend.

Figure 4

Evolution of the cumulative emitted electron lepton number (top), cumulative gain of muon lepton number in the PNS (middle), and cumulative energy loss (bottom) during the three main neutrino emission phases of Fig. 1 for our $1.44M_{\odot }$ models with different nuclear EOSs as indicated in the legend.

Figure 5

Relative differences between ${\overline{\nu }}_{\mu }$ and ${\overline{\nu }}_{\tau }$ emission and detection properties according to Eq. (1) for model 1.44-SFHo as in Fig. 2. Positive values mean that the quantity for ${\overline{\nu }}_{\mu }$ is larger than the average.

Figure 6

Postbounce evolution of the luminosities (top), cumulative emitted energies (middle), and mean energies of ${\overline{\nu }}_e$ and ${\overline{\nu }}_x$ for our 1.62-SFHo model including PNS convection and muons compared to model 1.62-SFHo-c without convection (but including muons; dashed lines in the left panels) and model 1.62-SFHo-m without muons (but including convection; dashed lines in the right panels). Note the change of the scale on the $x$-axis from linear to logarithmic at 1 s. The neutrino luminosities emitted at postbounce times $t_{\mathrm{pb}}>1\mathrm{s}$ are scaled by a factor of 5.

Figure 7

SN 1987A neutrino data at IMB, Kam-II, BUST and LSD. We show the detected positron energy as a function of time relative to the first event at IMB (7:35:41.374 UT on 23 February 1987). The first events of Kam-II and BUST are aligned with that of IMB because both detectors had a significant clock uncertainty. For BUST, we also show an earlier event that was attributed to background. LSD measured an additional burst nearly five hours earlier not shown here. In Kam-II, event No. 6 and those after 17 s as well as the late LSD events (another one at 37.5 s) are usually attributed to background. The fiducial masses shown for the scintillator detectors BUST and LSD are water equivalents. The data are listed in Tables 2, 3, 4, the overall detector properties in Table 6.

Figure 8

Detector properties. Top: Trigger efficiencies (for IMB with maximum uncertainties). Middle: Event spectrum for our fiducial SN ($T=4\mathrm{MeV}$), normalized to 1 kt water equivalent (5 kt for IMB). As a thin gray line, nearly identical with LSD, we show the event spectrum without threshold. This illustrative plot does not include “smearing” of the positron event energy by finite energy resolution of the detectors. Bottom: Background rate in Kam-II (total 0.187 Hz) and BUST (total 0.034 Hz) as function of reconstructed event energy. These background events have various sources, for example $\beta$ decay of ${}^{214}\mathrm{Bi}$ in Kam-II.

Figure 9

Allowed regions (95% CL) for the total and average ${\overline{\nu }}_e$ energy measured at different detectors, assuming a Maxwell-Boltzmann spectrum with $T=\overline{\epsilon }/3$. Joint region and best-fit value from $\mathrm{IMB}+\mathrm{Kam}\text{−}\mathrm{II}$ in green, from all experiments in magenta.

Figure 10

Confidence regions for all experiments combined, with (magenta) and without (blue) the late-time events, assuming a Maxwell-Boltzmann spectrum. We show 68% and 95% confidence regions as well as best-fit points.

Figure 11

Confidence regions (68% and 95%) and best-fit point (golden) if the three late Kam-II events are attributed to a Maxwell-Boltzmann flux originating from a SN fallback signal. Joint analysis from all experiments (notably two late BUST events) in blue.

Figure 12

Joint 95% confidence contours from all experiments for the shown values of the pinching parameter. Thick contours include all data, thin ones exclude the late-time events. Our model predictions are superimposed, ignoring flavor conversion, with different colors indicating the different PNS masses. The four groups with different symbols correspond to the different EOS models. The one-dimensional likelihoods marginalized over the complementary parameters are shown as a corner plot.

Figure 13

Impact of flavor conversion. Same confidence contours as in Fig. 12 in each panel. For each EOS we show the model predictions in a different panel for the different progenitor masses without (open circles) and with complete (plus signs) ${\overline{\nu }}_e–{\overline{\nu }}_x$ flavor swap.

Figure 14

Cumulative energy distributions in IMB, Kam-II, and BUST together with the expectations from our models for no-flavor swap (top row) and full-flavor swap (bottom row). The black dashed lines for Kam-II and BUST leave out the late events.

Figure 15

Expected signal durations in IMB and Kam-II, i.e., the time when 95% of the expected events have accrued, for all our SN models based on the ${\overline{\nu }}_e$ signal without flavor conversion. These results are also shown in Table 7, where the signal duration based on full-flavor swap is provided as well.

Figure 16

Cumulative event distributions in IMB, Kam-II, and BUST together with the expectations from our models. Time is measured relative to event No. 1 in each experiment, whereas the SN bounce time is shifted by $\delta t$ according to the best-fit values provided in Table 7 for each model. In BUST we include the background in the signal prediction, explaining the positive slope in the signal prediction even at late times. Upper two rows: Full signal duration, using the ${\overline{\nu }}_e$ or ${\overline{\nu }}_x$ flux in the rows as indicated (no- or full-flavor swap). In IMB, we use the best-fit trigger efficiency, explaining the smaller spread in total signal prediction. Bottom two rows: Same for the first second.

Figure 17

Differential event distribution (signal and background) at each experiment, compared with the observations. Results are shown for model 1.44-SFHo without flavor swap; the offset time for each experiment is chosen as the best-fit value reported in Table 7.

Figure 18

Expected late signal for our $1.44M_{\odot }$ models compared with background. We have assumed full-flavor swap (signal caused by ${\overline{\nu }}_x$) to maximize the predicted signal. Left: BUST. The vertical lines indicate the timing of the two late events. Right: Kam-II. We show the energy-integrated signal with $E_{{\overline{\nu }}_{\mu }}^{\det }\ge 7.6\mathrm{MeV}$, corresponding to $N_{\mathrm{hit}}\ge 20$, as solid lines and $E_{{\overline{\nu }}_{\mu }}^{\det }\ge 11.4\mathrm{MeV}$, corresponding to $N_{\mathrm{hit}}\ge 30$, as dashed lines. The vertical lines indicate the timing of the three late events.

Figure 19

Test statistic $\mathrm{\Lambda }$ for the different models, separately for each experiment, i.e., the log-likelihood relative to the maximum as defined in Eq. (c11). Late-time events are excluded. We show in gradual shades of colors the 68.3%, 95%, and 99.7% confidence levels. Signal caused by ${\overline{\nu }}_e$ (top row) or ${\overline{\nu }}_x$ (bottom row). One can only compare the models within one panel relative to each other, not between panels, because $\mathrm{\Lambda }$ is normalized to zero in each panel for the best case.

Figure 20

Same as Fig. 19 for all experiments combined, i.e., common likelihood as a product of the individual ones and also including the nonobservation at LSD. Results are shown both for the original ${\overline{\nu }}_e$ spectrum and for complete flavor swap.

Figure 21

Cumulative ${\overline{\nu }}_e$ event distributions at all experiments. The predictions for our $1.62M_{\odot }$ models are shown with (solid) and without (dashed) PNS convection, the experimental results of Kam-II and BUST with the late events included (solid) and excluded (dashed). For IMB, we choose for each model both the efficiency parameters and the time offset of the first event with respect to bounce that best fit the data. For Kam-II, we consider events integrated above 7.5 MeV to minimize the impact of the background; nevertheless, for a fair comparison, we do include the background integrated above this threshold energy. For BUST, we include the background spectrum without any threshold, explaining the increase of event number at late times.

Figure 22

Trigger efficiency in IMB. Data points from Ref. [187], fit function according to Eq. (a2) $\pm 0.05$ systematic uncertainty (dark gray band). For the broader gray band, the energy calibration uncertainty of $\pm 10\%$ is included. We also show the positron event spectrum from a fiducial SN with an assumed Maxwell-Boltzmann spectrum with $T=4\mathrm{MeV}$ (red bands for the different trigger efficiencies) and for a hypothetical 100% trigger efficiency (dashed). The positron spectra caused by the SN were multiplied by the indicated factors to fit the curves on a common scale. The hypothetical total event number under the dashed curve is 53.3, which is reduced to 6.4 after including the average trigger efficiency. These illustrative energy spectra do not include “smearing” by finite energy resolution.

Figure 23

Confidence regions (95%) and best-fit points for SN 1987A energy emission and average neutrino energy implied by the IMB data. The contours are for the maximally high or low and the average trigger efficiency.

Figure 24

Trigger efficiency in Kam-II following our fit function Eq. (a6). We also show the event spectrum from a fiducial SN with an assumed Maxwell-Boltzmann spectrum with $T=4\mathrm{MeV}$ (red solid line) and for hypothetically 100% trigger efficiency (dashed), leading to 14.0 (16.7) events. These illustrative energy spectra do not include “smearing” by finite energy resolution.

Figure 25

Background spectrum in Kam-II according to Ref. [33] (black dots) for a time interval of 10 s, yielding a total of 1.87 expected events. We also show our fit function Eq. (a7) together with its error Eq. (a8) as a one-sigma band, i.e., statistically around 68% of the data points for the ten-hour measurement period should be found within the gray band. (In Ref. [33] the corresponding error is shown for each data point.) Also shown is a “fiducial” SN signal with an assumed Maxwell-Boltzmann spectrum with $T=3\mathrm{MeV}$ (blue) and 4 MeV (red) that would yield a total of 9.0 (14.0) events. These illustrative energy spectra do not include “smearing” by finite energy resolution.

Figure 26

Trigger efficiency in BUST (Baksan) following the fit function Eq. (a9). We also show the event spectrum from a fiducial SN with an assumed Maxwell-Boltzmann spectrum with $T=4\mathrm{MeV}$ (red solid line) and for hypothetically 100% trigger efficiency (dashed), leading to 1.52 (2.19) events. These illustrative energy spectra do not include “smearing” by finite energy resolution.

Figure 27

Background spectrum in BUST according to [33] (black dots) for a time interval of 10 s, yielding a total 0.34 expected events. We also show our fit function Eq. (a10) with its error given in Eq. (a11) as a one-sigma gray band, i.e., the expected scatter of the data points for the ten-hour measurement period. (In Ref. [33] the corresponding error is shown for each data point.) Also shown is a “fiducial” SN signal with an assumed Maxwell-Boltzmann spectrum with $T=3\mathrm{MeV}$ (blue) and 4 MeV (red) that would yield a total of 0.93 (1.52) events. The illustrative predicted SN energy spectra do not include “smearing” by finite energy resolution. The background events refer directly to the reconstructed energy and no such smearing would be applied.

Figure 28

Trigger efficiency in LSD (Mont Blanc) following the fit function Eq. (a12). We also show the event spectrum from a fiducial SN with an assumed Maxwell-Boltzmann spectrum with $T=4\mathrm{MeV}$ (red solid line) and for hypothetically 100% trigger efficiency (dashed), leading to 0.962 (0.987) events. These illustrative energy spectra do not include “smearing” by finite energy resolution.

Figure 29

Distribution of scattering angles and energies of the IMB (black) and Kam-II (blue) events with approximate $1\sigma$ error regions, excluding the Kam-II event No. 6 which is likely background. Notice that the directional errors are for the scattering angle $\theta$, whereas here we show $\cos \theta$, leading to $1\sigma$ error ellipses that are strongly distorted near the forward or backward directions.

Figure 30

Charged-current neutrino cross sections per target particle. Solid lines for ${\overline{\nu }}_e$, dashed lines for ${\nu }_e$.

Figure 31

Results of the Kolmogorov-Smirnov test for the spectral shape of Kam-II neutrinos with our suite of models, up to a maximum time $t_{\text{cutoff}}$. We assume no offset between the first event and $t=0$ of our models.